We have two main approaches to perform POD: (1) the standard POD method, in which all domains, \(t\)  and \(\mathbf {\mu }\) , are compressed simultaneously (2) the nested POD technique, in which \(t\)  and \(\mathbf {\mu }\)  domains are compressed consecutively. In this work, we employ the latter since our \(N^t\)  is large (i.e., small-time-steps to satisfy Courant–Friedrichs–Lewy (CFL) condition, see Equation (REF )). Consequently, the SVD computation of the standard POD case may become unfeasible because it requires a large amount of resources, both in terms of CPU time and memory storage (i.e., the bottleneck is due to the simultaneous compression in \(t\)  and \(\mathbf {\mu }\) .). Moreover, from [1]}, the nested POD could provide comparable accuracy to the standard POD. We note that, in the reduced order modeling community, the nested POD can be also referred to as two-level POD or hierarchical approximate POD [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}. The detail of nested POD could be found in Appendix .
